Tides

• Tides


  Periodic raising and lowering of sea level that occurs daily throughout the ocean
• Isaac Newton’s gravitational laws explain the relationship with the lunar cycle (moon)
• Tides


  Are fundamentally very long and regular shallow water waves
• Gravitational force

  1. Proportional to the product of masses

  2. Inversely proportional to the square of the separation distance
• G is the gravitational constant, doesn’t change
• Greater mass, closer together


  Greater gravitational attraction
• Greatest force at zenith – closest to moon
• Least force at nadir – furthest from moon and opposite zenith
• Centripetal Forces


  Center-seeking force that connects an orbiting body to its parent, pulling the object inward toward the parent
• Gravity is the centripetal force that holds the Moon in orbit around Earth
• Resultant Forces

  Mathematical difference between gravitational and centripetal forces
• Tide Generating Forces


  • Resultant force has a significant horizontal component
  • Lunar bulges result when force pushes water into two simultaneous bulges, one toward the Moon and one away from the Moon
• If the Moon were stationary and aligned with the equator but the Earth still rotated about its axis, there would be two high and two low tides in one day
• Tidal period is the time between high tides
• Tides are always shallow-water waves
• Lunar day is the time between two successive overhead moons, which is 24 hours and 50 minutes
• Solar day is 24 hours, and high tides are 12 hours and 25 minutes apart
• Moon rises 50 minutes later each night, and high tides are 50 minutes later each day
• Tidal bulges caused by the Moon are similar to lunar bulges but much smaller due to the Moon being closer to Earth and exerting greater gravitational force
• Earth’s rotation

  • Flood tide – water moves toward shore
  • Ebb tide – water moves away from shore
  • Tidal bulges are fixed relative to the Sun’s and Moon’s positions, and Earth’s rotation carries specific locations into and out of tidal bulges, creating flood and ebb tides
• Monthly tidal cycle is 29.5 days because that’s how long it takes the Moon to complete an orbit around Earth
• Tidal range is the difference between high and low tides
• Syzygy is when the Moon, Earth, and Sun are aligned, and Quadrature is when the Moon is in the first or third quarter phase
• Spring tides occur during new or full moons when the tidal range is the greatest, while neap tides occur during quarter moons when the tidal range is the least
• Earth, Moon, and Sun aligned


  Quadrature - Moon in first or third quarter phase
• Monthly Tidal Cycle

  • Spring tides - New or full moons, Tidal range greatest
  • Neap tides - Quarter moons, Tidal range least
• Monthly tidal cycle is 29.5 days because that’s how long it takes Moon to complete an orbit around Earth
• Tidal range

  Difference between high and low tides
• Declination of the Moon and Sun: During most of the year, the Moon and Sun are not directly overhead at the equator
• Declination

  Angular distance above or below the equator
• Ecliptic


  Plane on which the Earth’s elliptical orbit around the Sun is located
• Earth’s rotation is tilted 23.5º with respect to the ecliptic (remember the seasons)
• Moon’s orbit is tilted 5º with respect to the ecliptic
• Maximum declination of the Moon with respect to the Earth’s equator is 28.5º (23.5 + 5)
• Declination changes between 28.5º north and 28.5º south during the year
• Monthly Tidal Cycle - Complicating Factors

  • Effects of Elliptical Orbits: Earth/Moon around Sun - Earth is closest to sun (perihelion) in N. Hemisphere Winter, Earth is farthest from sun (aphelion) in N. Hemisphere Summer, Spring tides have greater ranges during N. Hemisphere winter than in summer, Spring tides have greatest ranges when they coincide with perigee
• Declination of the Moon determines the position of the tidal bulges
• Any location, except the poles, will have two high tides and two low tides per lunar day
• Neither the two high tides nor the two low tides are of the same height because of the declination of the Moon and the Sun (except when the Moon and Sun are simultaneously above the equator)
• Monthly and yearly cycles of tidal range are related to the changing distances of the Moon and Sun from Earth